The present invention relates generally to earth boring and drilling, and more particularly to a method of and system for optimizing the rate of penetration in drilling operations.
It is very expensive to drill bore holes in the earth such as those made in connection with oil and gas wells. Oil and gas bearing formations are typically located thousands of feet below the surface of the earth. Accordingly, thousands of feet of rock must be drilled through in order to reach the producing formations.
The cost of drilling a well is primarily time dependent. Accordingly, the faster the desired penetration depth is achieved, the lower the cost in completing the well.
While many operations are required to drill and complete a well, perhaps the most important is the actual drilling of the bore hole. In order to achieve the optimum time of completion of a well, it is necessary to drill at the optimum rate of penetration. Rate of penetration depends on many factors, but a primary factor is weight on bit. As disclosed, for example in Millheim, et al., U.S. Pat. No. 4,535,972, rate of penetration increases with increasing weight on bit until a certain weight on bit is reached and then decreases with further weight on bit. Thus, there is generally a particular weight on bit that will achieve a maximum rate of penetration.
Drill bit manufacturers provide information with their bits on the recommended optimum weight on bit. However, the rate of penetration depends on many factors in addition to weight on bit. For example, the rate of penetration depends upon characteristics of the formation being drilled, the speed of rotation of the drill bit, and the rate of flow of the drilling fluid. Because of the complex nature of drilling, a weight on bit that is optimum for one set of conditions may not be optimum for another set of conditions.
One method for determining an optimum rate of penetration for a particular set of conditions is known as the xe2x80x9cdrill off testxe2x80x9d, disclosed, for example, in Bourdon, U.S. Pat. No. 4,886,129. Ignoring the effects of wall friction and hole deviation, as the drill string is lowered into the borehole, the entire weight of the drill string is supported by the hook. The drill string is somewhat elastic and it stretches under its own weight. When the bit contacts the bottom of the borehole, weight is transferred from the hook to the bit and the amount of drill string stretch is reduced. In a drill off test, an amount of weight greater than the expected optimum weight on bit is applied to the bit. While holding the drill string against vertical motion at the surface, the drill bit is rotated at the desired rotation rate and with the fluid pumps at the desired pressure. As the bit is rotated, the bit penetrates the formation. Since the drill string is held against vertical motion at the surface, weight is transfer from the bit to the hook as the bit penetrates the formation. By the application of Hooke""s law, as disclosed in Lubinsky U.S. Pat. No. 2,688,871, the instantaneous rate of penetration may be calculated from the instantaneous rate of change of weight on bit. By plotting bit rate of penetration against weight on bit during the drill off test, the optimum weight on bit can be determined. After the drill off test, the driller attempts to maintain the weight on bit at that optimum value.
A problem with using a drill off test to determine an optimum weight on bit is that the drill off test produces a static weight on bit value that is valid only for the particular set of conditions experienced during the test. Drilling conditions are complex and dynamic. Over the course of time, conditions change. As conditions change, the weight on bit determined in the drill off test may no longer be optimum.
Another problem is that there may be substantial friction between the drill pipe or drill collars and the wall of the bore hole. This friction, in effect, supports part of the weight of the string and makes the apparent weight on bit determined from surface measurements higher than the actual weight on bit. The bore hole wall and pipe friction problem is exaggerated in highly deviated holes in which the long portions of the drill pipe lie on and are supported by the wall of a nearly horizontal bore hole. Also, in high friction environments, the pipe tends to stick at various depths, which effectively decouples the hook from the bit. Thus, the driller is less able to control the weight on bit while drilling. While it is weight that causes the bit to penetrate the earth, in high friction environments, it is difficult to determine the actual weight on bit from surface measurements.
It is therefore an object of the present invention to provide a method and system for providing, dynamically and in real time, an optimum rate of penetration for a particular set of conditions.
The present invention provides a method of and system for optimizing bit rate of penetration while drilling. The method substantially continuously collects bit rate of penetration, weight on bit, pump or standpipe pressure, and rotary torque data during drilling. The method stores bit rate of penetration, weight on bit, pressure, and torque data in respective data arrays. Periodically, the method performs a linear regression of the data in each of the data arrays with bit rate of penetration as a response variable and weight on bit, pressure, and torque, respectively, as explanatory variables to produce weight on bit, pressure, and torque slope coefficients. The method also calculates correlation coefficients for the relationships between rate of penetration, and weight on bit, pressure, and torque, respectively. The method then selects the drilling parameter, i.e., weight on bit, pressure, or torque, with the strongest correlation to rate on penetration as the control variable.
The method periodically searches the data array for the control variable to determine a maximum rate of penetration. The depth of search into the data array is dependent on the value of the control variable slope coefficient. The more positive the control variable slope coefficient, the greater the depth of search into the data array. If the control variable slope coefficient is strongly negative, the method searches only a small distance into the data array.
The method bases the optimum control variable determination on a selected number of control variable values associated with the maximum rates of penetration within the depth of search and the control variable slope coefficient. The selected number depends on the depth of search. Generally, the greater the depth of search, the greater the selected number. If the selected number is greater than one, then the method averages the selected control variable values to obtain an average value. If the control variable slope coefficient is in a selected range near zero, the method sets the optimum control variable value at the average control variable value. If the control variable slope coefficient is greater than a selected positive value, the method sets the optimum control variable value at the average control variable value plus a selected increment. If the control variable slope coefficient is less than a selected negative value, the method sets the optimum control variable value at the weight on bit value minus a selected increment.